In an amazing interview with the showrunners from Homeland, Breaking Bad, New Girl, and Justified, Walking Dead showrunner Glen Mazzara finally revealed why Carl can't simply stay in the damn house. He explained as much in a roundtable with the Los Angeles Times:

What's the biggest argument you've had in the writers' room?

Mazzara: We will have different opinions, and there's a lot of debate about, you know, would a zombie do that? I wrote a scene in which a zombie climbed a ladder and everybody told me I was an idiot because zombies can't do that. I was, like, if I wrote it down it happens. And they're, like, no, no, no. So we cut that [...]

We had a debate about the young boy, Carl. And everyone wants to know why Carl's not in the house. Well, it's boring to sit in a house. And he's a little boy and he wants to mix it up and stuff. And he's walking through the woods and finds a zombie trapped in the mud and he starts doing what any Huck Finn would do and starts throwing rocks at the monster. And then later that is the same zombie that pulls itself free and kills Dale. And the writers were very nervous about that, you know? It feels earned, but it's a risk. Because Dale is a beloved character and if this other character is involved and responsible for that death, is the audience going to now hate Carl? But I thought the story was worth the chance.